A8299. Pairs of Numbers

重题请做P2090

Let's assume that we have a pair of numbers ( $a,b$ ). We can get a new pair ( $a+b,b$ ) or ( $a,a+b$ ) from the given pair in a single step.

Let the initial pair of numbers be (1,1). Your task is to find number $k$ , that is, the least number of steps needed to transform (1,1) into the pair where at least one number equals $n$ .

The input contains the only integer $n$ ( $1<=n<=10^{6}$ ).

The pair (1,1) can be transformed into a pair containing 5 in three moves: (1,1) $→$ (1,2) $→$ (3,2) $→$ (5,2).